Equilibrium analysis for a mass-conserving model in presence of cavitation

We study the existence of equilibrium positions for the load problem in Lubrication Theory. The problem consists of two surfaces in relative motion separated by a small distance filled by a lubricant. The system is described by the modified Reynolds equation (Elrod-Adams model) which describes the behavior of the lubricant and an extra integral equation given the balance of forces. The balance of forces allows to obtain the unknown position of the surfaces, defined with one degree of freedom.